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Question 838191: City Wide Delivery Service uses vans costing $24800 each. How much will the company have to invest today to accumulate enough money to buy six new vans at the end of 4 years? City Wide's bank is currently paying 12% interest compounded quarterly.
a)92727
b)24500
c)15000
d) 14525
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! each van costs 24,800
6 new vans will cost 24,800 * 6 = 148,800.
the number of years is 4.
the number of compounding periods per year is 4 (quarterly).
the number of time periods involved is therefore 4 * 4 = 16 quarterly time periods.
the annual interest rate is 12%.
if you pay interest rate quarterly, then the quarterly interest rate is 12% / 4 = 3% per quarter.
the decimal equivalent of 3% is .03
the formula you will use is:
f = p * (1 + r) ^ n
f is equal to the amount of money you will be paying for the vans in 4 years.
p is the amount of money you will need to today in order to do that.
r is equal to the quarterly compounding rate which is equal to .03.
n is equal to the number of quarterly compounding periods which is equal to 16.
the formula becomes:
148,800 = p * (1 + .03) ^ 16
this can be written as:
148800 = p * (1.03)^16
divide both sides of this equation by (1.03)^16 and you get:
148800 / (1.03)^16 = p
simplify to get:
148800 / 1.604706439 = p
simplify further to get:
p = 92727.24056
this can be written as:
p = $92,727.25 rounded to the next highest penny.
you will need to invest $92,727.25 today in order to have at least $148,800 in 4 years.
$92,727.25 invested at 3% per quarter for 16 quarters comes out to be:
92727.25 * (1.03)^16 which is equal to 148800.0152 which can be written as:
$148,800.02 rounded to the nearest penny.
your answer would be selection a which is 92727.
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